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Control theory: control path parameter estimation

First you have to define the control path. This is done by selecting the control element types in the table below. The parameters of the control elements are estimated with the differential evolution algorithm. The type of control elements that are part of the control path have to be guessed before.

Control path parameters

Number	Control element	Parameter K	Parameter T	Parameter D	Transfer function
1	none P PT1 PT2 dead time I D PD1
2	none P PT1 PT2 dead time I D PD1
3	none P PT1 PT2 dead time I D PD1
4	none P PT1 PT2 dead time I D PD1

Real control path step response measured data

The measurement data has to be entered in the text area in the form t, u, y (time, input signal, output signal).

0.01, 0, 0 0.02, 0, 0 0.03, 0, 0 0.04, 0, 0 0.05, 0, 0 0.06, 0, 0 0.07, 0, 0 0.08, 0, 0 0.09, 0, 0 0.1, 0, 0 0.11, 0, 0 0.12, 0, 0 0.13, 0, 0 0.14, 0, 0 0.15, 0, 0 0.16, 0, 0 0.17, 0, 0 0.18, 0, 0 0.19, 0, 0 0.2, 0, 0 0.21, 0, 0 0.22, 0, 0 0.23, 0, 0 0.24, 0, 0 0.25, 0, 0 0.26, 0, 0 0.27, 0, 0 0.28, 0, 0 0.29, 0, 0 0.3, 0, 0 0.31, 0, 0 0.32, 0, 0 0.33, 0, 0 0.34, 0, 0 0.35, 0, 0 0.36, 0, 0 0.37, 0, 0 0.38, 0, 0 0.39, 0, 0 0.4, 0, 0 0.41, 0, 0 0.42, 0, 0 0.43, 0, 0 0.44, 0, 0 0.45, 0, 0 0.46, 0, 0 0.47, 0, 0 0.48, 0, 0 0.49, 0, 0 0.5, 0, 0 0.51, 1, 0.00036478745854688 0.52, 1, 0.0014201086681386 0.53, 1, 0.0034525580838539 0.54, 1, 0.006709828552299 0.55, 1, 0.01140129688698 0.56, 1, 0.017698917761136 0.57, 1, 0.025738397763516 0.58, 1, 0.035620620674194 0.59, 1, 0.047413294551564 0.6, 1, 0.061152791061453 0.61, 1, 0.076846147606202 0.62, 1, 0.094473203205765 0.63, 1, 0.11398883972304 0.64, 1, 0.13532530088978 0.65, 1, 0.15839456265475 0.66, 1, 0.18309072961922 0.67, 1, 0.20929243372303 0.68, 1, 0.23686521287431 0.69, 1, 0.26566384885433 0.7, 1, 0.29553464555371 0.71, 1, 0.32631763038534 0.72, 1, 0.35784866355207 0.73, 1, 0.38996144170361 0.74, 1, 0.42248938437765 0.75, 1, 0.45526739346838 0.76, 1, 0.4881334777838 0.77, 1, 0.52093023652687 0.78, 1, 0.55350619725156 0.79, 1, 0.58571700548928 0.8, 1, 0.61742646480595 0.81, 1, 0.64850742752245 0.82, 1, 0.678842537707 0.83, 1, 0.70832482931742 0.84, 1, 0.73685818353221 0.85, 1, 0.76435765035587 0.86, 1, 0.79074964051501 0.87, 1, 0.81597199447579 0.88, 1, 0.83997393611034 0.89, 1, 0.86271591912105 0.9, 1, 0.88416937479921 0.91, 1, 0.90431637005154 0.92, 1, 0.9231491848782 0.93, 1, 0.94066981863449 0.94, 1, 0.95688943445929 0.95, 1, 0.97182775121431 0.96, 1, 0.98551239215369 0.97, 1, 0.99797819934155 0.98, 1, 1.009266522562 0.99, 1, 1.0194244911295 1, 1, 1.0285042766137 1.01, 1, 1.0365623540517 1.02, 1, 1.0436587687349 1.03, 1, 1.0498564151406 1.04, 1, 1.055220334032 1.05, 1, 1.059817033184 1.06, 1, 1.0637138366109 1.07, 1, 1.0669782665863 1.08, 1, 1.069677462154 1.09, 1, 1.071877637245 1.1, 1, 1.0736435809385 1.11, 1, 1.0750382018432 1.12, 1, 1.0761221180324 1.13, 1, 1.0769532934427 1.14, 1, 1.077586721153 1.15, 1, 1.0780741534923 1.16, 1, 1.0784638784865 1.17, 1, 1.0788005417569 1.18, 1, 1.0791250126079 1.19, 1, 1.0794742927168 1.2, 1, 1.079881465535 1.21, 1, 1.0803756842586 1.22, 1, 1.0809821959997 1.23, 1, 1.0817223996075 1.24, 1, 1.0826139344385 1.25, 1, 1.0836707972606 1.26, 1, 1.0849034843972 1.27, 1, 1.0863191561691 1.28, 1, 1.0879218206737 1.29, 1, 1.0897125339544 1.3, 1, 1.0916896136515 1.31, 1, 1.0938488632874 1.32, 1, 1.0961838044265 1.33, 1, 1.0986859140562 1.34, 1, 1.1013448646571 1.35, 1, 1.1041487645726 1.36, 1, 1.1070843964394 1.37, 1, 1.1101374516038 1.38, 1, 1.1132927586225 1.39, 1, 1.116534504123 1.4, 1, 1.1198464444856 1.41, 1, 1.1232121069914 1.42, 1, 1.1266149792679 1.43, 1, 1.1300386860511 1.44, 1, 1.1334671524614 1.45, 1, 1.1368847531712 1.46, 1, 1.1402764470132 1.47, 1, 1.1436278967422 1.48, 1, 1.1469255738225 1.49, 1, 1.1501568482583 1.5, 1, 1.1533100636239 1.51, 1, 1.1563745975777 1.52, 1, 1.1593409082608 1.53, 1, 1.162200567085 1.54, 1, 1.1649462785109 1.55, 1, 1.1675718874959 1.56, 1, 1.1700723753648 1.57, 1, 1.1724438449114 1.58, 1, 1.17468349559 1.59, 1, 1.176789589689 1.6, 1, 1.1787614104054 1.61, 1, 1.1805992127543 1.62, 1, 1.1823041682531 1.63, 1, 1.1838783043149 1.64, 1, 1.1853244392766 1.65, 1, 1.1866461139629 1.66, 1, 1.187847520665 1.67, 1, 1.1889334303756 1.68, 1, 1.1899091190838 1.69, 1, 1.1907802938916 1.7, 1, 1.1915530196601 1.71, 1, 1.1922336468482 1.72, 1, 1.192828741147 1.73, 1, 1.1933450154584 1.74, 1, 1.1937892647089 1.75, 1, 1.1941683039294 1.76, 1, 1.1944889099736 1.77, 1, 1.19475776719 1.78, 1, 1.1949814173012 1.79, 1, 1.1951662136931 1.8, 1, 1.1953182802575 1.81, 1, 1.1954434748815 1.82, 1, 1.1955473576283 1.83, 1, 1.1956351636037 1.84, 1, 1.1957117804626 1.85, 1, 1.1957817304679 1.86, 1, 1.1958491569757 1.87, 1, 1.1959178151896 1.88, 1, 1.195991066997 1.89, 1, 1.1960718796716 1.9, 1, 1.1961628282077 1.91, 1, 1.1962661010312 1.92, 1, 1.1963835088158 1.93, 1, 1.1965164961261 1.94, 1, 1.1966661555951 1.95, 1, 1.1968332443436 1.96, 1, 1.1970182023446 1.97, 1, 1.1972211724376 1.98, 1, 1.1974420217016 1.99, 1, 1.1976803639015 2, 1, 1.1979355827316 2.01, 1, 1.1982068555897 2.02, 1, 1.1984931776288 2.03, 1, 1.198793385845 2.04, 1, 1.1991061829794 2.05, 1, 1.1994301610234 2.06, 1, 1.1997638241385 2.07, 1, 1.2001056108151 2.08, 1, 1.2004539151181 2.09, 1, 1.2008071068811 2.1, 1, 1.2011635507328 2.11, 1, 1.2015216238556 2.12, 1, 1.2018797323972 2.13, 1, 1.2022363264704 2.14, 1, 1.2025899136962 2.15, 1, 1.2029390712617 2.16, 1, 1.2032824564781 2.17, 1, 1.2036188158408 2.18, 1, 1.2039469926068 2.19, 1, 1.2042659329172 2.2, 1, 1.2045746905048 2.21, 1, 1.2048724300372 2.22, 1, 1.205158429154 2.23, 1, 1.2054320792677 2.24, 1, 1.2056928852021 2.25, 1, 1.2059404637495 2.26, 1, 1.2061745412323 2.27, 1, 1.2063949501587 2.28, 1, 1.2066016250635 2.29, 1, 1.2067945976284 2.3, 1, 1.2069739911755 2.31, 1, 1.2071400146273 2.32, 1, 1.2072929560266 2.33, 1, 1.207433175706 2.34, 1, 1.2075610991948 2.35, 1, 1.2076772099493 2.36, 1, 1.2077820419848 2.37, 1, 1.2078761724876 2.38, 1, 1.2079602144768 2.39, 1, 1.2080348095836 2.4, 1, 1.2081006210078 2.41, 1, 1.2081583267064 2.42, 1, 1.2082086128649 2.43, 1, 1.2082521676936 2.44, 1, 1.2082896755866 2.45, 1, 1.2083218116753 2.46, 1, 1.2083492368025 2.47, 1, 1.2083725929361 2.48, 1, 1.2083924990395 2.49, 1, 1.2084095474053 2.5, 1, 1.2084243004591 2.51, 1, 1.2084372880323 2.52, 1, 1.2084490050989 2.53, 1, 1.208459909969 2.54, 1, 1.2084704229246 2.55, 1, 1.2084809252847 2.56, 1, 1.2084917588781 2.57, 1, 1.2085032259047 2.58, 1, 1.2085155891609 2.59, 1, 1.2085290726039 2.6, 1, 1.2085438622272 2.61, 1, 1.2085601072205 2.62, 1, 1.2085779213844 2.63, 1, 1.2085973847692 2.64, 1, 1.2086185455109 2.65, 1, 1.2086414218322 2.66, 1, 1.2086660041811 2.67, 1, 1.2086922574771 2.68, 1, 1.2087201234387 2.69, 1, 1.2087495229645 2.7, 1, 1.2087803585433 2.71, 1, 1.2088125166677 2.72, 1, 1.2088458702306 2.73, 1, 1.2088802808823 2.74, 1, 1.2089156013293 2.75, 1, 1.2089516775582 2.76, 1, 1.2089883509676 2.77, 1, 1.2090254603956 2.78, 1, 1.2090628440314 2.79, 1, 1.2091003411988 2.8, 1, 1.2091377940065 2.81, 1, 1.209175048856 2.82, 1, 1.2092119578048 2.83, 1, 1.2092483797801 2.84, 1, 1.2092841816428 2.85, 1, 1.2093192391015 2.86, 1, 1.2093534374774 2.87, 1, 1.2093866723245 2.88, 1, 1.2094188499064 2.89, 1, 1.2094498875378 2.9, 1, 1.209479713794 2.91, 1, 1.2095082685969 2.92, 1, 1.2095355031838 2.93, 1, 1.2095613799683 2.94, 1, 1.2095858723004 2.95, 1, 1.2096089641365 2.96, 1, 1.2096306496262 2.97, 1, 1.2096509326284 2.98, 1, 1.2096698261623 2.99, 1, 1.2096873518058 3, 1, 1.2097035390498 3.01, 1, 1.2097184246159 3.02, 1, 1.2097320517483 3.03, 1, 1.2097444694876 3.04, 1, 1.2097557319346 3.05, 1, 1.209765897511 3.06, 1, 1.2097750282259 3.07, 1, 1.2097831889532 3.08, 1, 1.2097904467263 3.09, 1, 1.2097968700566 3.1, 1, 1.2098025282793 3.11, 1, 1.2098074909323 3.12, 1, 1.2098118271703 3.13, 1, 1.2098156052192 3.14, 1, 1.2098188918722 3.15, 1, 1.2098217520298 3.16, 1, 1.2098242482849 3.17, 1, 1.2098264405553 3.18, 1, 1.2098283857626 3.19, 1, 1.2098301375578 3.2, 1, 1.209831746094 3.21, 1, 1.2098332578442 3.22, 1, 1.209834715464 3.23, 1, 1.2098361576968 3.24, 1, 1.2098376193203 3.25, 1, 1.2098391311315 3.26, 1, 1.2098407199685 3.27, 1, 1.2098424087666 3.28, 1, 1.2098442166449 3.29, 1, 1.2098461590218 3.3, 1, 1.2098482477567 3.31, 1, 1.209850491313 3.32, 1, 1.2098528949422 3.33, 1, 1.2098554608834 3.34, 1, 1.2098581885779 3.35, 1, 1.2098610748936 3.36, 1, 1.2098641143583 3.37, 1, 1.2098672993979 3.38, 1, 1.2098706205783 3.39, 1, 1.2098740668472 3.4, 1, 1.2098776257739 3.41, 1, 1.2098812837866 3.42, 1, 1.209885026402 3.43, 1, 1.2098888384491 3.44, 1, 1.209892704283 3.45, 1, 1.2098966079887 3.46, 1, 1.2099005335726 3.47, 1, 1.2099044651421 3.48, 1, 1.2099083870715 3.49, 1, 1.2099122841536 3.5, 1, 1.2099161417366 3.51, 1, 1.2099199458467 3.52, 1, 1.2099236832952 3.53, 1, 1.2099273417707 3.54, 1, 1.2099309099162 3.55, 1, 1.2099343773921 3.56, 1, 1.2099377349243 3.57, 1, 1.2099409743395 3.58, 1, 1.209944088586 3.59, 1, 1.2099470717439 3.6, 1, 1.2099499190215 3.61, 1, 1.2099526267426 3.62, 1, 1.2099551923226 3.63, 1, 1.209957614236 3.64, 1, 1.2099598919754 3.65, 1, 1.2099620260038 3.66, 1, 1.209964017699 3.67, 1, 1.209965869295 3.68, 1, 1.2099675838164 3.69, 1, 1.209969165011 3.7, 1, 1.2099706172791 3.71, 1, 1.2099719456006 3.72, 1, 1.2099731554616 3.73, 1, 1.2099742527806 3.74, 1, 1.2099752438351 3.75, 1, 1.2099761351891 3.76, 1, 1.2099769336228 3.77, 1, 1.2099776460642 3.78, 1, 1.2099782795235 3.79, 1, 1.2099788410312 3.8, 1, 1.209979337579 3.81, 1, 1.2099797760655 3.82, 1, 1.2099801632454 3.83, 1, 1.2099805056834 3.84, 1, 1.2099808097128 3.85, 1, 1.2099810813983 3.86, 1, 1.209981326504 3.87, 1, 1.2099815504655 3.88, 1, 1.2099817583675 3.89, 1, 1.2099819549251 3.9, 1, 1.2099821444702 3.91, 1, 1.2099823309416 3.92, 1, 1.2099825178799 3.93, 1, 1.2099827084257 3.94, 1, 1.2099829053218 3.95, 1, 1.2099831109186 3.96, 1, 1.2099833271829 3.97, 1, 1.2099835557094 3.98, 1, 1.2099837977346 3.99, 1, 1.2099840541535 4, 1, 1.2099843255374 4.01, 1, 1.2099846121545

Step response simulation parameters

Step height
Step time
Simulation end time
Maximum number of iteration steps

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Download source code of the used algorithms.